\(R_{\rm clust}\)  is a constant parameter of dimension \({\rm yr}^{-1} {\rm Gpc}^{-3}\)  which encodes the clustering properties of PBHs. In the following, we consider \(R_{\rm clust}\)  as a free parameter in our model and, unless stated otherwise, we fix it by requiring that the integral of the merger rate at \(z=0\)  over the mass range \([5,\,100]\,M_\odot \)  gives a total rate of \(\sim 38\,{\rm yr}^{-1}\,{\rm Mpc}^{-3}\) ,
consistent with the edge of the 1\(\sigma \)  constraint on the local merger rate inferred from GWTC-2 [1]}. We note that the parameter governing the amplitude of the merger rate is actually \(R_{\rm clust}\,(f_{\rm PBH}^{\rm tot})^2\)  and \(R_{\rm clust}\)  is thus degenerate with the the total fraction of PBHs, as also noted in Refs. [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. However, since we normalize \(f_{\rm PBH}^{\rm tot}=1\) , we break this degeneracy by hand.
<FIGURE>